Periodic electrostatically focused beam tubes



May 30, 1961 F. E. vAccARo ET A/L 2,986,672

PERIODIC ELECTROSTATICALLY FocusED BEAM TUBES Filed Deo. 16, 1958 3 Sheets-Sheet 1 PERIODIC ELECTROSTATICALLY FOCUSED BEAM TUBES Filed DSC. 16, 1958 May 30, 1961 F. E. vAccARo ET AL 5 Sheets-Sheet 2 Z f. WMM W MMMWM www1. IWC., .w EW KH ma. PM fwy 8 as@ May 30, 1961 F. E. vAccARo r-:T AL 2,986,672

PERIODIC ELECTROSTATICALLY FocUsED BEAM TUBES Filed Dec. 16, 1958 3 Sheets-Sheet 3 65 65' j j 45 l5' la' if l INVENTOR.

BIM/@WM #GENT PERIODIC ELECTROSTATICALLY FOCUSED l BEAM TUBES Frank E. Vaccaro and Wieslaw W. Siekanowicz, New Brunswick, NJ., assignors to Radio Corporation of America, a corporation of Delaware Filed Dec. 16, 195s, ser. No. 780,733

16 Claims. (Cl. sis-5.34)

This invention relates to electron beam devices, and particularly, to such devices having periodic electrostatic means for focusing the beam.

It is well known in the art that an electron beam of appreciable length and current density will spread or diverge due to mutual repulsion of the like negative charges on theelectrons unless means are provided to confine the beam. Thus, it is conventional to provide beam tubes, such as klystrons and traveling wave tubes, with magnetic or electrostatic beam focusing means. In many cases, it is highly desirable, if not necessary, that the beam diameter be maintained constant at least along the R.F. interaction region. `It is possible to maintain a substantially constant beam diameter by means of a constant magnetic eld having ux lines parallel to the beam axis if a very high magnetic eld strength is provided. However not only is the structure for providing such a magnetic eld too heavy for use in light weight equipment, but also the cost of producing the required magnetic field is high. Accordingly, thel trend has been toward the use of periodic magnetic or electrostatic focusing means wherein the beam is repeatedly focused by a series of altemately-directed magnetic or electrostatic focusing lenses distributed along the beam path. Such periodic focusing structures have the advantages of light rweight and low operating cost. However, periodic electrostatic focusing means heretofore used do not subject the team to a uniform restraining force along the beam path, and therefore, fail to maintain a constant beam diameter. Examples of periodic magnetic and electrostatic focusing means are illustrated on pages 208 and 209, respectively, of the textbook Theory and Design of Electron Beams, by J. R. Pierce, published by D.'Van Nostrand Co., Inc. in 1954. As shown by Pierce, the beam diameter varies considerably, being scalloped with the same periodicity as the magnets or electrodes making up the periodic lens system.

Accordingly, the principal object of-the present inven tion is to provide a periodic electrostatic beam-focusing means that will maintain the diameter of the beam substantially constant along an extended beam path.

Another object is to provide an improved periodic beam focusing electrode structure.

In accordance with the invention, the diameter of the beam in an electron beam device is maintained substantially constant by establishing a periodic electrostatic focusing viield along the beam path having substantially the same potential variation between given minimum and maximum potentials in each half-period along the path that would exist along an electron stream having innite transverse dimensions and the same current density passing at right angles through a pair of grids maintained at the given minimum and maximum potentials. This desiredpotential variation has been closely approximated by mounting a multiplicity of very thin apertured plates in alignment along the beam path in each period and applying a separatepotential to each plate. However, a Amore practical arrangement comprises a set of apertured plate electrodes at a high potential alternating along the beam path with a set of elongated hollow electrodes at a low potential suitably shaped internally to approximate the desired potential variation. The best approximation of the ideal potential variation is obtained when each of the focusing electrodes is provided with a grid extending across the beam path. The electron beam can be introduced at one end of the periodic focusing structure at the desired diameter by any conventional means, such as aV parallel-flow gun or a convergent-How gun, as shown on pages 178 and 189 of the Pierce textbook referred to above. s

In the drawings:

Fig. 1 is a schematic representation to be referred to.

in explaining the invention;

(Fig. 2 is a graph showing the potential variation bei-'- tween two grids in a theoretical electron device having/an electron flow of iniinite transverse dimension;

Fig. 3 is a graph showing the normalized current unde the conditions of Fig. 2 as a function of the voltage of-4 the lower potential grid, for a given high potentialgrid.

voltage;

Fig. 4 is a graph showing the normalized perveance as a function of the voltage of the lower potential grid;

of alternative focusing electrode structures which may be substituted for the focusing electrode structure shown in F ig. 5, in accordance with the invention; y

Fig. 9 is a graph showing the potential variations obtained in an electrolytic tank for the focusing structures shown in Figs. 6, 7 and 8, respectively, in comparison with the ideal variation shown in Fig. 2; v l Fig. 10 is an axial sectional view of a tw0CeVi2Yk1y stron tube having a convergent-now gun and incorporating the present invention; and

Fig. 11 is an axial sectional view of the gun portion o f a klystron similar to that shown in Fig. 10 but having a parallel-How gun. ...f

In designing tubes utilizing electrostatic elds for contning an electron beam to some specified diameter, it is desired to obtain maximum current and perveance with minimum scalloping at the boundary of the beam. The smallest possible degree of scalloping is desirable to reduce the current intercepted by the electrodes and to realize maximum gain for a given beam current.

Realization of parallel laminar llow will be discussed with reference to Fig. l, which schematically showsa series of grids G having infinite dimensions normal to an x coordinate. Assume that alternate grids are connected together, and that one set of grids is maintained at a Agiven low positive D.C. potential V1, and the other set at a given high positive D.C. potential VH. In the absence of space charge (zero current) the potential distribution between the two grids is linear, as shown by the dashed straight line A in Fig. 1. If an electron stream having innite transverse dimensions, uniform current density and elec.- tron trajectories parallel to the x axis is injected at the initial plane OL, the presence of space charge will depress the potential between the grids. In Fig. 1, the curve B represents the actual potential variation in an electron ow of infinite width between adjacent grids under the' condition: v

o V x 92:0 (l) that is, `when the rateof change of potential with distance x along the path of the electron stream at the low poten tial grid is zero. As explained on pages 248-259 of the textbook Vacuum Tubes, by K. R. Spangenbcrg, Mt` Graw-Hill, 1948, the potential variationunder theseon;

Patented May 30, 1.961.

ditions in any region LH can be determined from the following equation:

VH=the high potential r=2.335 106 amperes per volt 3/2 J =the current density in amperes per square meter 'Ihe curve for Equation 2 is plotted in Fig. 2. The slope of this curve is zero at x= and increases continuously with x up to the high potential grid, thus the curve resembles a parabola and may be considered parabolic in shape.

As shown in Fig. l, the potential distribution (curve B) in each of regions HL is a mirror image of the parabolic curve in the regions LH. The entire potential distribution curve B is made up of a series of double-parabolic sections joined together with a cusp, or abrupt change in sign of the slope of the curve, at each high potential plane. Because the transverse dimensions are infinite, the variation of the D.C. potential in the transverse direction (r) is zero, i.e.:

Equation 2 can be transformed mathematically to the following equation:

3/.4 Figi-- 5 which is the well-known equation for a space-chargesaturated diode with infinite plane electrodes.

Thus, it can be seen from Equation 5 that ,the term x0 in .Equation 2 is the distance over which a `potential VL will vproduce a current density I in a space-charge-saturated diode having an anodepotential VL.

The present invention is based on the concept that an electron beam of finite dimensions could be perfectly confined or focused to maintain constant dimensions along an extended path if one could establish vthe same parabolic potential variation along the beam path that exists in the hypothetical infinite-grid model shown in Fig. l. It is, of course, .impossible to exactly duplicate this ideal .condition along a beam of finite dimensions. However, `it will .be shown how to closely approximate the ideal condition by utilizing periodic electrostatic focusing structure that will establish a satisfactory potential variation that does not differ substantially from the ideal potential variation of Fig. l as shown by curve B.

The design of a beam tube containing a round or ribbon-type electron beam having finite transverse dimensions .but still substantially satisfying the conditions described `above for an infinite stream follows a procedure similar to that used for designing Pierce-type electron `guus. Thus, itis necessary toestablishat the boundary between the beam and the space-charge-free region sub stantially the same parabolic potential distribution that would exist if the beam extended to infinity in a transverse direction. In the charge-free region the potential must satisfy Laplaces equation subject to the boundary conditions given by Equations 2 and 3. This reasoning is similar to that described on page 179 in Pierces book referred to above. The total current I in a round beam is then:

X104' amperes where d is the beam diameter and S is the period of the focusing structure. Similarly, for a ribbon beam having width w and thickness t, the current I is:

IOTG amperes If VH and the dimensions of the beam are constant, and the low voltage, VL, is varied, the relative variation of the beam current as a function of the voltage ratio VL/VH is shown in Fig. 3. The equation for this curve is:

Maximum beam current, Im, will be obtained when VL/VH= 0.25. Hence, for a round beam:

tively, the electron transittime and phase shift per period. The transit time is given :by:

TzgLs/z) (ll) where:

and 1r=the charge to mass ratio of the electron. The effective velocity, ue, computed on the basis of transit time is:

The effective-voltage, Ve, is:

I sa

l e (14 .i

When Equations 2, ll, 12, 13 and 14 .are combined, the effective voltage is:

If the perveanceP is defined as I/ Veit/2, IEquations 6 and l5 can be combined to give:

The `maximum .perveance, Pm, occurs when VL :equals zero, hence:

X10-f' `amparos per volti .I (i) escasas Fig. 4 shows a plot of normalized perveance, P/Pm, as' a function of VL/VH.

Fig. 5 schematically shows an experimental electron beam -tube that was constructed to verify the theory on which the invention is based. The tube comprises an elongated vacuum envelope 1 containing an electron gun 3 at one end and a collector 5 at the other end, defining an extended beam path therebetween. The gun 3 comprises a large-area concave cathode 7, heater 9, focusing electrode 11 and two accelerating electrodes 13 and 15 arranged to produce an electron beam converging from a large cross sectional area at the cathode to a given smaller area in the plane of the second accelerating electrode 15 where the convergent action of the gun is overcome by space charge forces to produce substantially parallel ow.

In order to confine the beam to maintain parallel ow atfsubstantially constant diameter beyond the plane of electrode 15, there is provided, a periodic electrostatic focusing structure made up of a multiplicity of identical thin apertured plate focusing electrodes 17 which are mounted close together in alignment along the beam path between electrode 15 and collector 5. As shown in Fig. 5, electrode 15, which is also a thin apertured plate, serves also as the first electrode of the iirst period of the focusing structure. Electrode 15 is connected to the 8th, 16th, 24th, 32nd, 40th, and 48th electrodes 17 and to an external D.C. voltage source 18 to establish a high potential, VH, at each end of each period. Similarly, each intermediate electrode 17 in each period is connected to corresponding electrodes 17 in the other periods and connected to external leads to permit the establishment of any desired potential distribution, VH--VL-VH, within each period, as shown by the potential curve in Fig. 5.

In accordance with the present invention, the focusing electrodes 15 and 17 were connected to voltage sources providing a parabolic potential distribution V(x) in each period as determined from Equation 4 for a given minimum potential VL and a given beam current density I. For a beam having a diameter approximately 65% of the diameter of the apertures in electrodes 15 and 17, an overall current transmission to the collector of about 99% was obtained, indicating a loss of only 1% collected by the focusing structure.

The design of shaped focusing electrodes approximating the ideal boundary conditions of Equation 4 at the edge of the beam for a smaller member of electrodes per period can be determined by use of an electrolytic tank technique similar to that used for designing Pierce-type electron guns (see pages 179 and 180 of the Pierce textbook referred to above). There is a large number of electrode shapes which will approximate the ideal boundary conditions, and several specific electrode shapes will bev disclosed as examples only.

The ideal boundary conditions require that Equations 3 and 4 be satisfied throughout the region occupied by the beam. Measurements made in an electrolytic tank have shown that these conditions can be very closely approximated by electrodes of the shapes shown in Fig. 6 for each period of an alternative periodic focusing structure to be substituted for the focusing electrodes 15 and 17 of Fig. 5.

. In- Fig. 6, electrodes 15 and 17 are essentially the same as the corresponding high potential electrodes at the beginning and end of each period in Fig. 5. The (seven) intermediate electrodes 17 in each period in Fig. 5 are replaced by a single annular low potential electrode 19 having a double-conical inner surface 21 with a minimum diameter at lthe central plane equal to the diameter of the aperture in the plate electrodes 15 and 17 and not substantially larger than the beam diameter d. In order to establish the same potential across the beam, a thin mesh grid 23 is mounted across the beam path in the :central plane of each electrode, as shown. The length 6 of each period is about 1.7 times the beam diameter d. Annular electrode 19 has an axial length of about .8d and a maximum inner diameter at each end of about 1.6d. The minimum thickness of the plate electrodes 15 and 17 is about .03d. The potential distribution obtained in the electrolytic tank using the electrode shapes shown in Fig. 6 is plotted with dots 16 in Fig. 9 for comparison with the ideal curve 20 of Fig. 2. As shown, the dots almost coincide with the ideal curve.

In many applications grids are undesirable because they intercept current and limit the beam power density. Removal of the low potential grids will improve the current transmission. Removal of the high potential gridswill improve both current transmission and the beam power density. For this reason, it is preferable to omit the grids 23 in Fig. 6 and obtain a slightly poorer approximation tothe ideal focusing field as is usually done in electron guns. A compromise design in which gridsjareused only at the high potential planes will show improved current transmission and a relatively good approximation to the ideal potential distribution. Figs. 7 and 8 show two gridless electrode structures similar to that shown in Fig. 6 and approximating the ideal boundary conditions.

In Fig. 7, the inner diameter of the beam apertures in the focusing electrodes 15', 17 and 19' is 1.34 times the beam diameter d and the period is 2.3d. The low potential electrode 19 has an axial length of about 1.25d and a maximum inner diameter at each end of about 1.74d. The thickness of the high potential electrode is about .14d. The potential distribution obtained with the electrodes of Fig. 7 is shown as the short-dash curve 18 in Fig. 9.

In Fig. 8, the aperture diameter is 1.7d and the period is 2.9d. The low potential electrode 19" has a length of 1.73d and a maximum inner diameter of 1.9ld. 'The thickness of electrodes 15 and 17" is about .15d. The potential distribution obtained with the electrodes of Fig'. 8 is shown as the long-dash curve 22 in Fig. 9.

The ideal potential distribution at the beam boundary is shown as the solid curve in Fig. 9. In order to ap'- proach the ideal boundary conditions in a structure without grids, the period should be at least 1.5d and the beam diameter should be at least one half of the electrode aperture diameter. lIn practice, however, to obtain high gain and efliciency in traveling wave tube or klystron applications, it is desirable to use a large ratio of beam to aperture diameter. In these cases the gridless elec'- trodes can closely approximate the ideal potential .distribution at the beam boundary. In each of the examples shown in Figs. 6 to 8, the difference between the maximum and minimum inner diameters of the elongated low potential electrodes 19 is less than the minimum inner diameter.

In order to make a preliminary current transmission test on the focusing electrode structure shown in Fig. 8', potentials were applied to the focusing electrodes 15, 17 in the tube shown in Fig. 5 to establish the potential distribution of the long-dash curve of Fig. 9. Also, for comparison, the potential distribution for a structure like that of Fig. 8 except that the low potential electrode 19" had a cylindrical (instead of double-conical) inner surface was applied to the focusing electrodes of Fig. 5. A current transmission of 97% was obtained with the potential distribution for the shaped electrodes of Fig. 8, as compared to 86% obtained with the potential distribution for the cylindrical structure. The perveance, P, of the structure of Fig. 8, as calculated from the formula P=I/Ve3/2 was about 4.4 as compared to 4.1 lcalculated for the cylindrical structure. Y 4

Fig. lO shows the present invention incorporated, Lfor example, in a two-cavity klystron tube. The tube comprises, from left to right, a convergent-flow electron `gun 25, an input or velocity modulating cavity ,resonatorAZIL an elongated drift tube structure 29, an output cavity resonator 31, and a collector 33. The electron gun 25 comprises a large-area concave cathode 35, heater 37, focusing electrode 39 and accelerating electrodes 41 and 43-arranged to inject a high density parallel-flow beam into the input resonator 27. The outer peripheries of the gun electrodes are interposed between and sealed to ceramic rings 45 to provide insulation therebetween and form part of the vacuum envelope of the tube. The gun 2S is mounted on the input resonator 27 by another ceramic ring 47. Similarly, the collector 33 is mounted on the output resonator 31 by a ceramic ring 49.

In accordance with the invention, the drift tube structure 29 and the beam apertures in the input and output resonators 27 and 31 are formed as a series of periodic beam focusing electrodes of the kind shown in Figs. 6 to 8. As in Fig. 5, the nal accelerating electrode 43 of the gun also forms the rst high potential focusing electrode. The focusing electrodes comprise a set of annular low potential electrodes 51 having double-conical inner surfaces like electrode 19 in Figs. 6 to 8 alternating with apertured plate high potential electrodes S3. The first two of electrodes 51 are mounted through the walls of the input resonator 27, and the last two are similarly mounted in the output resonator 31. The first and last of electrodes 53 are mounted in the resonators 27 and 31, respectively.

Each of the plate electrodes 53 in the drift tube region is mechanically connected to each adjacent annular electrode 51 in insulated and sealed relation by means of an apertured ceramic disc 55 sealed at its inner edge to the outer surface of electrode 51 and at its outer periphery to a metal ring 57 sealed to the electrode 53 and having an inner ange 58.

Each of the annular electrodes 51 in the drift region is provided at each end with an apertured disc 59 extending outwardly to about the inner edge of the ange 58 of the nearest ring 57. The radial dimension of each disc 59 and the flange 58 of each ring 57 is made approximately a quarter wavelength at the operating frequency of the tube, so that the quarter wave open line formed by the disc 59 and electrode 53 combined with the quarter wave closed line formed by the ring 57 and electrode S3 will form a broadband radiofrequency short circuit between adjacent electrodes 51 and 53. Each of the plate electrodes 53 in the input and output resonators is similarly mounted by radiofrequency choke made up of a ceramic ring 61 and flanged discs 63 and 65, to produce a wideband radiofrequency short circuit in the plane of disc 65. Each of the input and output resonators 27 and 31 is provided with a radiofrequency coupling means, such as a coupling loop 66.

Fig. l1 is a fragmentary view of a modification of Fig. 10, in which a parallel-how gun 67 is used. The gun 67 comprises a plane cathode 69, a heater 71, and a focusing electrode 73, with ceramic rings 75. The rst annular low `potential electrode 51 of Fig. 10 is replaced by an annular electrode A'77 having a single diverging conical inner surface, which electrode serves as the sole accelerating electrode of the gun and also as the low potential electrode of a starting half period of the periodic focusing system, as shown by the potential curve in Fig. 1l. This potential curve also shows the diode distribution between the cathode and electrode 77.

Fig. 1l also shows a modified choke mounting for the high potential plate electrode in the input resonator 78, which comprises a pair of apertured ceramic discs 79, a first pair of flanged rings 81 and a second pair of flanged rings 83. The resonator 78 is provided with suitable radiofrequency coupling means (not shown). The remainder of the tube of Fig. 11 is essentially the Same as that of Fig. 10.

What is claimed is:

1. An electron beam tube comprising an electron gun f or producing an electron beam of given ,transverse k,dimensions `t a ,given transverse Platte elena .an extended beam path, and means including a series of spaced focusing electrodes aligned along said path beyond Said plane for establishing along said path a periodic electrostatic focusing field having a plurality of periods and having substantially the same parabolic potential variation between given transverse planes of minimum and maximum potential in each half-period at the boundary of said beam as an electron ow along said path having infinite transverse dimensions and the same current density pass ing at right angles through a pair of grids maintained at said given minimum and maximum potential planes, for maintaining said beam dimensions substantially constant beyond said rst named plane.

2. A n electron beam tube comprising an electron gun for producing an electron beam of given dimensions at a given transverse plane along an extended beam path, and means including a series of spaced focusing electrodes aligned along said path beyond said plane for establishing along said path a periodic electrostatic focusing iield having a plurality of periods with a parabolic potential variation V(x) in each period, at least at the boundary of said beam, substantially determined by the equation:

where VL=the minimum value of the potential in each period,

V(x) :the potential in a plane at a distance x from the plane of VL, where x a half period,

ixl=the absolute value of x,

a2=2.335 105 amperes per volt3/2,

J=the current density of the beam in amperes per square meter,

for maintaining said beam dimensions substantially constant beyond said first named plane.

3. A beam tube as in claim l, wherein said means in cludes a grid extending across said beam path at each plane of maximum potential.

4. A beam tube as in claim 3, further including a grid extending across the beam path at each plane of minimum potential.

5. A beam tube as in claim l, wherein said series of focusing electrodes comprises a first set of high potential apertured plate electrodes alternating with a second set of low potential elongated hollow electrodes, the inner surface of each of said hollow electrodes increasing from a minimum dimension near the center to a larger dimension at each end.

6. A beam tube as in claim 5, wherein said beam has a circular cross section of given beam diameter at said first-named plane, and said inner surface of each of said hollow electrodes is double-conical.

7. A beam tube as in claim 6, wherein the minimum diameter of said focusing electrodes is not more than twice the beam diameter, and the length of each period is at least 1.5 times the beam diameter.

8. A beam tube as in claim 7, wherein the minimum diameter of said focusing electrodes is not substantially greater than the beam diameter, and the length of each period is about l.7 times the beam diameter.

9. A beam tube as in claim 8, wherein each of said hollow electrodes has an axial length about 0.8 times the beam diameter and a maximum inner diameter at each end about 1.6 times the beam diameter, and the thickness of each of said plate electrodes is not greater`than about 0.03 times the beam diameter.

l0. A beam tube as in claim 7, wherein the minimum diameter of said focusing electrodes is about 1.34 times the beam diameter, and the length of each period is about 2.3 times the beam diameter.

l1. A beam tube as in claim 10, wherein each of said hollow electrodes has an axial length about 1.25 times the `beam `diameter and a 4maximum inner diameter at 9 each end about 1.74 times the beam diameter, and the thickness of each of said plate electrodes is about 0.14 times the beam diameter.

12. An electron beam tube comprising an electron gun for producing an electron beam of given diameter at a given transverse plane along an extended beam path, and periodic electrostatic focusing means extending for a plurality of periods along said path for confining said beam to-,substantially constant diameter along said path beyond said plane; said means comprising a series of apertured plate electrodes having the same inner diameter alternating along said beam path with a series of elongated annular electrodes each having a minimum inner diameter equal to said first-named inner diameter near the center and increasing to a larger diameter at each end.

13. An electron beam tube as in claim 12, wherein the minimum inner diameter of said electrodes is not more than twice the beam diameter, and the length of each period is at least 1.5 times the beam diameter.

14. An electron beam tube as in claim 13, comprising a velocity modulating cavity resonator coupled to said beam path near the beginning of said focusing means,

and an output cavity resonator coupled to said beam path near the other end of said focusing means.

15. An electron beam tube as in claim 1, wherein said series of focusing electrodes comprises a multiplicity of identical thin apertured plates mounted close together in lalignment along said beam path, and said means further includes a D.C. voltage source connected to said plates for applying suitable potentials thereto to approximate said parabolic potential distribution at the boundary of said beam.

16. An electron beam tube as in claim 12, wherein the diierence between said larger and said minimum inner diameters of said elongated electrodes is less than said minimum inner diameter.

References Cited in the le of this patent UNITED STATES PATENTS 2,289,071 Ramo July 7, 1942 2,610,306 Touraton et al. Sept. 9, 1952 2,843,793 Ashkin July 15, 1958 

